How to reach an unresponsive potential client?

I also have had this happen. Since the M&G date has come and gone and you reached out to your first client with no response, go with your 2nd client. I don't bother with anyone who won't respond after a couple of attempts within a week. Even if they finally contact me - without a good reason, "I" don't want them for a customer as they end up wasting my time and taking advantage of their drop and pick up times. I do a lot of repeat business with owners in Professional positions and they understand and respect the fact that this is a business and just as important as their employment/business.

I had something similar happen to me in the past with a non-Rover client. I reached out multiple times through multiple formats, and received no response. I finally sent one last message (through multiple channels) that if I did not hear from her by X day and time, I was going to have to open those days up to other clients.
As long as you are crystal clear about the deadline, and make numerous attempts, I think it's reasonable for you to drop the unresponsive owner for the one who is willing to give you their business. We are running businesses here, and I, for one, cannot financially afford to keep someone on the schedule who will not confirm their booking. I usually only book one family at a time, so if I hold that spot for them, and then they don't show, that could be a lot of potential revenue lost.

This happens to me pretty frequently. As long as you let the unresponsive client know you have another client for those dates, move on and make that booking! I've had people who act interested, then I don't hear from them and they were just hedging their bets and someone they know stepped up to watch the dog. I did just have a booked client not repsond to my texts, picked up the phone and got him. Some people are not up with the current texting communication.